Clearest quality format for UV images
Recommended: 


png: Great image quality, alpha support. File size is a bit large. Best overall. Compression hardly noticeable. also supports
tga: Popular in game engines. Good quality, alpha channel. Support for lossless compression.
hdr: 32 bit color depth. Use for environments maps only
exr: 32 bit color depth. Use it for rendering out images from blender that you plan on compositing later. Or for large textures that actually have the appropriate color information.
jpeg/jpg: Small file size, needs to use good compression to no like bad. 


NOT Recommended:


gif: png was created to replace gif
bmp: Huge file sizes